If the question is posed at the time Bill enters the class, she may ask the monitor, "How many [students
are/have been] late
thus/so far?"
If Jack is the fifth, Bill is the fourth, Jane is the third, Eddie is the second, etc., I can't offer much help. Tell 'em to take a number when they come in.
I'd have to ask, "Was Jane the second or the third or the fourth student to to enter the class late?"
Or perhaps better, since it wouldn't take either the teacher or the monitor any longer, she could guess: "Was Bill the second to come in late?" (reply) "No, he was the fourth."